VAR, SVAR & VECM Services
When several time series influence one another—interest rates, output, prices, credit—a single-equation model cannot capture the feedback. Vector autoregression treats them as an interdependent system, tracing how a shock to one variable ripples through the others over time.
A vector autoregression (VAR) models several time series jointly, letting each depend on its own past and the past of the others—capturing their dynamic interdependence. Structural VAR (SVAR) adds economic restrictions to identify meaningful shocks, and a vector error-correction model (VECM) is the form used when the series are cointegrated, combining long-run equilibrium with short-run dynamics.
What VAR models do
Many economic and financial variables are mutually dependent: interest rates affect output, output affects prices, prices feed back into rates. A single-equation model that treats one as the outcome and the rest as fixed predictors misses this feedback. A vector autoregression (VAR) instead models several time series jointly—every variable is allowed to depend on its own lagged values and the lagged values of all the others—so the system captures how the variables move together and influence one another over time.
The most useful outputs of a VAR are not the raw coefficients but three system-level tools. Impulse response functions (IRFs) trace how a one-off shock to one variable propagates through the whole system over subsequent periods—the signature VAR result. Forecast error variance decomposition (FEVD) attributes the variability of each variable to shocks from each source, showing which variables drive which. And Granger causality tests whether one variable’s past helps predict another’s future. Together these turn a system of equations into interpretable statements about dynamics and influence.
SVAR, VECM, and the family
A plain (reduced-form) VAR describes correlations among the variables’ shocks but does not, by itself, identify economically meaningful shocks. A structural VAR (SVAR) adds identifying restrictions—grounded in theory (for example, short-run, long-run, or sign restrictions)—so that the impulse responses can be interpreted as responses to specific structural shocks, such as a monetary-policy or supply shock. The credibility of an SVAR rests entirely on the plausibility of those restrictions, which we state and justify.
When the series are cointegrated (they share a long-run equilibrium), the appropriate form is a vector error-correction model (VECM), which combines the long-run relationships with short-run dynamics and adjustment. The wider family extends further: Bayesian VAR (BVAR) helps when many variables strain the data (large systems); time-varying-parameter VAR (TVP-VAR) lets relationships evolve over time; Markov-switching models allow distinct regimes (for example, crisis vs normal); and state-space models handle unobserved components and time variation. For causality where the integration and cointegration properties are awkward, the Toda–Yamamoto procedure provides a robust alternative to standard Granger tests. We select the member of the family that matches the data and the question.
Which VAR-family model fits
| Model | Use when | Gives you |
|---|---|---|
| Reduced-form VAR | Stationary variables, dynamics of interest | IRFs, FEVD, Granger causality |
| SVAR | You need economically meaningful shocks | Structural impulse responses |
| VECM | Variables are cointegrated (I(1)) | Long-run + short-run dynamics |
| Bayesian VAR | Many variables, limited data | Stable estimates for large systems |
| TVP-VAR / Markov-switching | Relationships change or switch regime | Time-varying or regime-dependent dynamics |
Specifying and identifying a VAR credibly
Sound VAR work rests on a sequence of decisions. Stationarity and cointegration come first: a VAR in levels, a VAR in differences, and a VECM are appropriate in different cases, and which is correct depends on the integration and cointegration properties of the series—so unit-root and cointegration testing precede the model, not follow it. Lag length is then chosen with information criteria and checked so that the residuals are free of serial correlation. Stability (the estimated system must be stationary) and residual diagnostics are verified before any interpretation.
The decisive issue for an SVAR is identification: extracting structural shocks requires restrictions that the data alone cannot supply, so they must come from theory and be defended. Different restriction schemes (recursive/Cholesky ordering, short- or long-run, or sign restrictions) can give different answers, and the ordering in a recursive scheme is itself an assumption—we make the scheme explicit, justify it, and check robustness to alternatives. For causality, standard Granger tests can be invalid when variables are integrated or cointegrated; the Toda–Yamamoto approach is used in those cases. And Granger causality is predictive precedence, not proof of a causal mechanism—a distinction we keep clear.
SVAR results are only as credible as their identifying restrictions—and Granger causality is not causation. Structural shocks require assumptions the data cannot supply, so the identification scheme must be justified and its robustness checked. “Granger causality” means predictive precedence, not a proven causal mechanism.
Software
We deliver the VAR family in established, reproducible tools—R, EViews, and Stata (with Bayesian and TVP-VAR estimation where needed)—covering unit-root and cointegration testing, lag selection, stability and residual diagnostics, identified impulse responses with confidence bands, FEVD, and Granger/Toda–Yamamoto causality, with versioned code.
How we deliver a VAR / SVAR / VECM study
This work sits within our wider econometrics practice—so the model form matches the data’s integration properties, the identification is justified, and the diagnostics are reported in full.
We start by testing stationarity and cointegration to determine the correct form (VAR in levels or differences, or a VECM), then select lag length and verify stability and residual diagnostics. For an SVAR we specify and justify the identification scheme; for causality we use Granger or Toda–Yamamoto as the data require; and for large systems, changing relationships, or regimes we use Bayesian, TVP, or Markov-switching variants.
Reporting sets out the pre-tests, the model and lag choice, the identification scheme and its justification, the diagnostics, and the impulse responses, FEVD, and causality results—so the dynamics can be judged, not just displayed.
You receive the estimated system with impulse response functions and confidence bands, forecast error variance decompositions, the Granger/Toda–Yamamoto causality results, the identification scheme and robustness checks, the stability and residual diagnostics, and reproducible analytical code and analysis-ready files (where appropriate and permitted).
VAR modelling across Management & Allied Studies
Systems of interacting time series are central to macroeconomics and finance—so the VAR family is a core toolkit across the quantitative disciplines we serve.
Macroeconomics & Monetary Policy
The classic VAR/SVAR setting—tracing how policy, output, and price shocks propagate through the economy over time.
Finance & Financial Markets
Interdependence and spillovers among asset prices, volatility, rates, and markets, including regime-switching dynamics.
Energy & Commodity Markets
Dynamic relationships among energy prices, output, and macro variables, often with structural or sign restrictions.
Banking & Credit
Transmission among credit, money, policy, and real variables, and how shocks pass through the system.
International & Development Economics
Cross-country and cross-market linkages and shock transmission in systems of macro-financial series.
Economic Policy & Forecasting
System forecasting and scenario analysis, including large Bayesian VARs for many-variable settings.
VAR, SVAR & VECM: common questions
Modelling a system of interacting time series?
When variables move together and feed back on one another, the VAR family captures the dynamics—impulse responses, variance decompositions, and causality—with the model form matched to the data and the identification justified.